Altermagnetic Lieb Lattice

Altermagnetism, characterized by alternating spin structures in reciprocal space, has recently emerged as a novel magnetic phase beyond the conventional categories of ferromagnetism and antiferromagnetism. Unlike ferromagnets, which possess finite net magnetization, and antiferromagnets, where opposite magnetic moments typically cancel to preserve Kramers degeneracy through translation-time-reversal or inversion-time-reversal symmetry, altermagnets exhibit zero net magnetization yet display symmetry-enforced spin polarization patterns in reciprocal space. This arises from the interplay between crystal rotational symmetry and magnetic ordering, endowing altermagnets with a variety of unique properties. This presentation will focus on altermagnetic Lieb lattices, covering their theoretical foundations, material realizations, and associated exotic physical phenomena. The first part will provide an introduction to altermagnetism and Lieb lattices, along with the theoretical basis of altermagnetic Lieb systems. The second part will discuss the emergence of alter-piezo responses in these lattices. The third part will introduce a topologically protected pseudo-degree of freedom—the axial degree of freedom—and demonstrate its realization in altermagnetic Lieb systems, together with the corresponding experimentally detectable axial Hall effect.